Engineering, 11.03.2020 22:58 only1123
Air flows steadily through a turbine that produces 3.5x 105 ft-lbf/s of work. Using the data below at the inlet and outlet, where the inlet is 10 feet below the outlet, please calculate the heat transferred in units of BTU/hr. You may assume steady flow and ignore viscous work.
Answers: 1
.
, shaft work rate is 
, rate of accumulation of energy inside control volume is 
, rate of work accomplished in viscous effects at the surface is 
, and the net energy efflux from the control volume is 
![\begin{array}{l}\frac{\delta Q}{d t}-\frac{\delta W_{s}}{d t}=\rho v A\left[e+\frac{P}{\rho}\right]_{2}-\rho v A\left[e+\frac{P}{\rho}\right] \\=\rho_{1} Q\left[u_{2}-u_{1}+\frac{v_{2}^{2}-v_{1}^{2}}{2}+\left(P_{2} / \rho_{2}-P_{1} / \rho_{1}\right)+g\left(z_{2}-z_{1}\right)\right] \\=\rho_{1} A_{1} v_{1}\left[u_{2}-u_{1}+\frac{v_{2}^{2}-v_{1}^{2}}{2}+\left(P_{2} / \rho_{2}-P_{1} / \rho_{1}\right)+g\left(z_{2}-z_{1}\right)\right]\end{array}](/tpl/images/0543/5935/d37d2.png)
internal energy at exit section is 
 volumetric flow rate is Q, inlet fluid density is 
, outlet fluid density is 
, specific energy is e, exit velocity is 
, inlet velocity is 
, inlet pressure is 
, outlet pressure is 
, acceleration due to gravity is g and distance between inlet and outlet is z.
![\frac{\delta Q}{d t}-\frac{\delta W_{s}}{d t}=\rho_{1} A_{1} v_{1}\left[u_{2}-u_{1}+\frac{v_{2}^{2}-v_{1}^{2}}{2}+\left(P_{2} / \rho_{2}-P_{1} / \rho_{1}\right)+g\left(z_{2}-z_{1}\right)\right]](/tpl/images/0543/5935/54105.png)
![\begin{aligned}&\frac{\delta Q}{d t}=\left(9.98 \times 10^{5}+3.5 \times 10^{5}\right) \mathrm{ftlb}_{\mathrm{f}} / \mathrm{s}\\&=13.48 \times 10^{5} \mathrm{ftb}_{\mathrm{f}} / \mathrm{s}\left[\frac{1 \mathrm{Ba}}{778.17 \mathrm{ftbr}}\right]\left[\frac{3600 \mathrm{s}}{1 \mathrm{hr}}\right]\\&=6.23 \times 10^{6} \mathrm{Btu} / \mathrm{hr}\end{aligned}](/tpl/images/0543/5935/32b1b.png)
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Air flows steadily through a turbine that produces 3.5x 105 ft-lbf/s of work. Using the data below a...
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